New Books in Mathematics

A true understanding of the pervasive role of software in the world demands an awareness of the volume and variety of real-world software failures and their consequences. No more thorough survey of these events may be available than Thomas Huckle and Tobias Neckel's Bits and Bugs: A Scientific and Historical Review of Software Failures in Computational Science (SIAM, 2019). Their book organizing an extensive collection of episodes into eight chapters that expand on an array of flavors of failures, increasing in intricacy from precision and rounding errors to the software–hardware interface and problems that emerge from complexity.

As I see it, this book serves three audiences: Instructors of computer engineering or numerical methods will find an educational text uniquely suited to a focus on software failures; software engineers will find an equally unique reference text; and students of the practice or the history of computational science will find a fully blazed trail through these complicated stories. Dr. Huckle joined me to discuss his and his coauthor's motivations for assembling the book, a sampler of the chapter headliners, and some of his thoughts on new and evolving computational tools with their own attendant opportunities for failure.

Technical readers will appreciate the mathematical excursions that rigorously introduce topics essential to understanding each chapter's headlining episodes, the exercises and MATLAB code provided at the book's website, and links to sources at Dr. Huckle's website. I found value in the recurring lesson that real-world failures arise from the coincidence of multiple, often multitudinous errors, as well as in the authors' consistent emphasis on the real human toll that the study of these errors is driven to prevent. That said, all readers may appreciate the fanciful taxonomy given in the introduction and the amusing (though sometimes apocryphal) idiosyncratic failures surveyed in the appendix.

Suggested companion works:



Thomas Huckle completed a degree program in mathematics and physics education and in pure mathematics, received a doctorate in 1985, and acquired his postdoctoral teaching qualification (habiliation) in 1991 at the University of Würzburg. A German research Foundation (DFG) grant enabled him to spend time performing research at Stanford University (1993–1994). In 1995 Professor Huckle joined TUM as professor of scientific computing. He has also been a member of the Mathematics Faculty since 1997. His primary research area is numerical linear algebra and its application in fields such as informatics and physics. His work focuses on solving linear problems on parallel computers, image processing and reconstruction, partial differential equations, and structured matrices.

Tobias Neckel has studied applied mathematics at the Technical University of Munich (TUM) and received a doctorate in Computer Science at TUM in 2009. He is currently senior researcher in scientific computing at TUM and has conducted research at the École Polytechnique, France (2003), the Tokyo Institute of Technology (2008), and the Australian National University (2017). His research interests include the numerical solution of differential equations, hierarchic and adaptive methods, uncertainty quantification, and various aspects of high-performance computing.

Cory Brunson is an Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data.

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Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas?

This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. David Sulzer, also known in the musical world as Dave Soldier, explains why the perception of music encompasses the physics of sound, the functions of the ear and deep-brain auditory pathways, and the physiology of emotion. He delves into topics such as the math by which musical scales, rhythms, tuning, and harmonies are derived, from the days of Pythagoras to technological manipulation of sound waves. Sulzer ranges from styles from around the world to canonical composers to hip-hop, the history of experimental music, and animal sound by songbirds, cetaceans, bats, and insects. He makes accessible a vast range of material, helping readers discover the universal principles behind the music they find meaningful.

Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind: The Physics and Neuroscience of Music (Columbia UP, 2021) demystifies how music works while testifying to its beauty and wonder.

Galina Limorenko is a doctoral candidate in Neuroscience with a focus on biochemistry and molecular biology of neurodegenerative diseases at EPFL in Switzerland. To discuss and propose the book for an interview you can reach her at [email protected].

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One pervasive stereotype about mathematics is that it is objective, unbiased, or otherwise exempt from the influence of human passions. James Wynn and G. Mitchell Reyes's edited collection will be a revelation even to mathematics professionals who don't take this strict view. The essays in Arguing with Numbers: The Intersections of Rhetoric and Mathematics (The Pennsylvania State UP, 2021) explore the interplays between rhetoric and mathematics that have shaped scholarly and popular culture through to the present day.

Opening the collection are both an historical sketch of scholarship at the intersection of these disciplines, from their division in ancient Greece to their hesitant reunion since the mid-twentieth century, and also a taxonomy of modern research into three distinct approaches, which we review in our discussion. The remaining essays use these approaches to probe the impact of mathematical rhetoric on the sciences (including Hantaro Nakaoka's analogical "Saturnian" model of atomic spectra), on cultural norms and institutions (including the influence of David X. Li's Gaussian copula on the behavior of financial markets), and on relations between mathematics professionals and the lay public. This last part contains a chapter on the legacy of the National Council of Teachers of Mathematics that highlights the importance to mathematics professionals of understanding the rhetorical dimensions of our discipline.

Bookending our discussion, Drs. Wynn and Reyes related the story of their edited collection, which makes the point that a cross-disciplinary exchange is needed to help both disciplines better understand their connections to each other and more responsibly manage those connections. Their suggestions will resonate with mathematicians interested in challenging narratives of objectivity, in diversifying our ranks, and in developing responsible rules and principles for the use of social and personal data. The analytical tools demonstrated in this book abet this effort.

Suggested companion works:

James Wynn is Associate Professor of English at Carnegie Mellon University. He is the author of Citizen Science in the Digital Age: Rhetoric, Science, and Public Engagement and Evolution by the Numbers: The Origins of Mathematical Argument in Biology.

G. Mitchell Reyes is Professor of Rhetoric and Media Studies at Lewis and Clark College. He is author of Stranger Relations: Mathematics, Rhetoric, and the Translative Force of Mathematical Discourse (in press with Penn State University Press) and coeditor of Global Memoryscapes: Contesting Remembrance in a Transnational Age.

Cory Brunson is an Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data.

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The Joy of Mathematics is based on an in-depth filmed conversation between Howard Burton and Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick and bestselling science and science fiction writer. For Ian Stewart, mathematics is far more than dreary arithmetic, while mathematical thinking is one of the most important—and overlooked—aspects of contemporary society. This wide-ranging conversation explores what mathematics is and why it’s worth doing, symmetry, networks and patterns, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, linking mathematical oscillations to animal gaits, how to deal with the peculiarities of the mathematical community, and much more.

Howard Burton is the founder of the Ideas Roadshow, Ideas on Film and host of the Ideas Roadshow Podcast. He can be reached at [email protected].

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Students and their families face a consequential choice in whether to pursue a degree, and in what area. For those considering mathematics programs, the choice may be particularly fraught: A gulf separates the exploratory and experimental mathematics done by professionals from the computational training of most secondary schools, and this can obscure the meanings of program options. Meanwhile, cultural anxieties and stereotypes can dissuade students who would flourish in mathematical careers. This despite mathematical professionals being among the most satisfied and well-compensated in their careers.

In Why Study Mathematics? (2020), Vicky Neale provides a compact guide to this juncture, which i expect students and their families and teachers will find hugely valuable. As part of the London Publishing Partnership's "Why Study" series, her book in Part I explores in detail the substance and varieties of math degrees, how students can shape them to their needs and interests, and what those who complete them go on to do after. For Part II, Neale gives the reader a deeper view into a selection of subfields and the work their practitioners do, including the technologically vital study of data compression and the (for now) more humanistic study of abstract networks known as Ramsey theory.

Dr. Neale has exceptional experience and skill as a mentor that comes through as she addresses questions that, in my experience, often aren't: Are mathematics degrees mostly for mathematically adept students? Once in a program, whom should i get to know? Where are all the job postings for "mathematician"? It was a treat to hear her expound further on the book, and i would suggest that anyone at the beginning of their professional life, with interest, aptitude, or just curiosity about mathematics, seek out this resource (or recommend it to their mentors and guidance offices!) as they weigh their options.

Suggested companion works:

Vicky Neale is the Whitehead Lecturer at the Mathematical Institute, University of Oxford, and a Supernumerary Fellow at Balliol College. She teaches pure mathematics to undergraduates, and combines this with work on public engagement with mathematics: she gives public lectures, leads workshops with school students, and has appeared on numerous BBC radio and television programmes. One of her current interests is in using knitting and crochet to explore mathematical ideas. She is the author of Closing the Gap: The Quest to Understand Prime Numbers (Oxford University Press, 2017)—listen to her interview with Jim Stein about that book here.

Cory Brunson is an Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data.

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Our universe might appear chaotic, but deep down it's simply a myriad of rules working independently to create patterns of action, force, and consequence. In Ten Patterns That Explain the Universe (MIT Press, 2021), Brian Clegg explores the phenomena that make up the very fabric of our world by examining ten essential sequenced systems. From diagrams that show the deep relationships between space and time to the quantum behaviors that rule the way that matter and light interact, Clegg shows how these patterns provide a unique view of the physical world and its fundamental workings.

Guiding readers on a tour of our world and the universe beyond, Clegg describes the cosmic microwave background, sometimes called the "echo of the big bang," and how it offers clues to the universe's beginnings; the diagrams that illustrate Einstein's revelation of the intertwined nature of space and time; the particle trail patterns revealed by the Large Hadron Collider and other accelerators; and the simple-looking patterns that predict quantum behavior (and decorated Richard Feynman's van). Clegg explains how the periodic table reflects the underlying pattern of the configuration of atoms, discusses the power of the number line, demonstrates the explanatory uses of tree diagrams, and more.

Galina Limorenko is a doctoral candidate in Neuroscience with a focus on biochemistry and molecular biology of neurodegenerative diseases at EPFL in Switzerland. To discuss and propose the book for an interview you can reach her at [email protected].

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As algorithms become ever more significant to and embedded in our everyday lives, ever more accessible introductions to them are needed. While several excellent technical and critical treatments have emerged in recent years, i had not come across a book for the general public that would provide a deep sense for the intuitions and motivations behind their development. Chris Bleakley's new book offers this and more: conceptual rigor woven into historical vignettes in a style that i believe general readers will find truly enjoyable to read.

Poems that Solve Puzzles: The History and Science of Algorithms (Oxford UP, 2020) is itself a quite poetic book, in which echoes of ideas and variations on themes can be heard throughout. Its stories encompass the early hypothetical and mechanical computers, the charactered rise of weather forecasting, the origins (and lulls) of machine learning, and the sensational competitions between master game players and artificial intelligence. The book traverses a long historical arc, but each episode is a quick read, remarkable in their ability to convey depth and rigor in crisp, plain language. It was a delight to talk with Chris about these and other aspects of his book.

Suggested companion works:

--Simon Singh, The Code Book

--George Dyson, Turing's Cathedral: The Origins of the Digital Universe

--Greg Kohs (director), "AlphaGo"

Chris Bleakley is Head of the School of Computer Science at University College Dublin. He graduated with a BSc (Hons) degree in Computer Science from Queen's University, Belfast, and a PhD degree in Electronic Engineering from Dublin City University. After college, he was employed as a software consultant by Accenture and, later, as a senior telecommunications researcher at Broadcom Eireann Research.

Cory Brunson is an Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data.

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Alfred S. Posamentier's Math Tricks: The Surprising Wonders of Shapes and Numbers (Prometheus Books, 2021) has a lovely assortment of puzzles from all areas of mathematics. Some will be familiar to many readers, but there are plenty of ones I’d never seen before – and I’ve seen lots of them. Some are at just the right level to intrigue students who may be put off by the dry way a lot of math courses are taught – and this alone is enough to make any parent consider having the book available when their child says that they hate math. Math is valuable not just because we can use it to balance our checking account or send rockets to the moon, but because it helps us think – and this book presents a lot of math in a very appealing fashion.

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Math Renaissance: Growing Math Circles, Changing Classrooms, and Creating Sustainable Math Education (Natural Math, 2018) couples two educational memoirs: Student Rachel Steinig brings her experience from diverse schooling models, surveys of teachers and fellow students, and selections of peer-reviewed scholarship to an examination of math instruction in the United States. Her chapters seek to locate root causes, transcend conventional advice, and inspire readers to imagine radical alternatives. Teacher Rodi Steinig invites readers into the role of leading math circles with detailed play-by-plays from her own experience. These chapters evince the importance (and interplay) in this role of background knowledge, preparation, compassion, and improvisation—and, perhaps most saliently for beginning teachers, of resisting the urge to rescue.

Taken together, the book critiques the existing systems that provide children's math education and drills down on an alternative model whose popularity continues to grow. Among my favorite parts of the book were Rodi's self-reflective thought bubbles on her performance facilitating math circles and Rachel's chapter on math instruction from a human rights perspective. The book is intended for teachers and parents of school-age children, though i think middle and high school students and even casual readers would find value in this forthright, thorough, and readable work. It was an absolute delight to discuss the book with both its authors!

Suggested Companion Works:

Rochelle Gutiérrez, Rehumanizing Mathematics: A Vision for the Future

Francis Su, Mathematics for Human Flourishing

Donald Finkel, Teaching with Your Mouth Shut

Robert Kaplan and Ellen Kaplan, Out of the Labyrinth: Setting Mathematics Free

Dave Auckly, Bob Klein, Amanda Serenevy, Tatiana Shubin, Inspiring Mathematics: Lessons from the Navajo Nation Math Circles

Rodi Steinig is an educator, author, and teacher trainer who has educated K-12 students in an inquiry-based approach for over twenty years. She founded the Math Renaissance Math Circle in 2011 hoping to awaken children’s inner mathematicians, to shepherd the unfolding of their abstract reasoning, and to disabuse them of the notion that math is the study of memorizing a bunch of facts and algorithms.

Rachel recently graduated from the University of Pennsylvania with a B.A. in Political Science. She is currently a Border Rights Project Fellow at the nonprofit Al Otro Lado, providing legal services to asylum-seekers at the border in Tijuana.

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Sixteen of today's greatest unsolved mathematical puzzles in a story-driven, illustrated volume that invites readers to peek over the edge of the unknown.

Most people think of mathematics as a set of useful tools designed to answer analytical questions, beginning with simple arithmetic and ending with advanced calculus. But, as Mage Merlin's Unsolved Mathematical Mysteries (MIT Press, 2020) shows, mathematics is filled with intriguing mysteries that take us to the edge of the unknown. This richly illustrated, story-driven volume presents sixteen of today's greatest unsolved mathematical puzzles, all understandable by anyone with elementary math skills. These intriguing mysteries are presented to readers as puzzles that have time-traveled from Camelot, preserved in the notebook of Merlin, the wise magician in King Arthur's court.

Our guide is Mage Maryam (named in honor of the brilliant young mathematician, the late Maryam Mirzakhani), a distant descendant of Merlin. Maryam introduces the mysteries—each of which is presented across two beautifully illustrated pages—and provides mathematical and historical context afterward. We find Merlin confronting mathematical puzzles involving tinker toys (a present for Camelot's princesses from the sorceress Morgana), cake-slicing at a festival, Lancelot's labyrinth, a vault for the Holy Grail, and more. Each mystery is a sword awaiting removal from its stone, capturing the beauty and power of mathematics.

Galina Limorenko is a doctoral candidate in Neuroscience with a focus on biochemistry and molecular biology of neurodegenerative diseases at EPFL in Switzerland. To discuss and propose the book for an interview you can reach her at [email protected].

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